document.write( "Question 271128: My son is in Honors Algebra in the 8th grade. I'm trying to help him figure this problem out but can't seem to get it. Please help.\r
\n" ); document.write( "\n" ); document.write( "If Alex gives Bobby $4, then Alex would have half as much money as Bobby. If Bobby gives Chris $7, then Chris would have $35 more than Bobby. If Chris gives Alex $17, then Alex would have $1 more than Chris.
\n" ); document.write( "How many dollars does each person have?\r
\n" ); document.write( "\n" ); document.write( "Thanks for your assistance.\r
\n" ); document.write( "\n" ); document.write( "Sincerely,\r
\n" ); document.write( "\n" ); document.write( "Will Schultz
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Algebra.Com's Answer #198548 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
let a = amount of money alex has originally.
\n" ); document.write( "let b = amount of money bobby has originally.
\n" ); document.write( "let c = amount of money chris has originally.\r
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\n" ); document.write( "\n" ); document.write( "If Alex give Bobby $4, then Alex would have half as much money as Bobby.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Equation we get is:\r
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\n" ); document.write( "\n" ); document.write( "(a-4) = (b+4)/2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "multiply both sides of these equations by 2 to get:\r
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\n" ); document.write( "\n" ); document.write( "2a-8 = b+4\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "subtract 4 from both sides of this equations to get:\r
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\n" ); document.write( "\n" ); document.write( "b = 2a-12\r
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\n" ); document.write( "\n" ); document.write( "If Bobby gives Chris 7, then Chris would have $35 more than Bobby.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "equation we get is:\r
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\n" ); document.write( "\n" ); document.write( "(c+7) = (b-7) + 35\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "subtract 7 from both sides of this equation to get:\r
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\n" ); document.write( "\n" ); document.write( "c = b-7+35-7 which becomes:\r
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\n" ); document.write( "\n" ); document.write( "c = b + 21\r
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\n" ); document.write( "\n" ); document.write( "If Chris gives Alex 17, then Alex would have 1 more than Chris.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Equation we get is:\r
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\n" ); document.write( "\n" ); document.write( "a+17 = c-17 + 1\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "subtract 17 from both sides of this equation to get:\r
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\n" ); document.write( "\n" ); document.write( "a = c-17+1-17 which becomes:\r
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\n" ); document.write( "\n" ); document.write( "a = c-33\r
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\n" ); document.write( "\n" ); document.write( "We have 3 equations to work with.\r
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\n" ); document.write( "\n" ); document.write( "They are:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "b = 2a-12 (first equation)
\n" ); document.write( "c = b + 21 (second equation)
\n" ); document.write( "a = c-33 (third equation)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "substitute 2a-12 for b in the second equation to get:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "c = (2a-12) + 21 which becomes:
\n" ); document.write( "c = 2a-12+21 which becomes:
\n" ); document.write( "c = 2a + 9\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "substitute 2a+9 for c in the third equation to get:\r
\n" ); document.write( "\n" ); document.write( "a = (2a+9)-33 which becomes:
\n" ); document.write( "a = 2a+9-33 which becomes:
\n" ); document.write( "a = 2a-24\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "subtract a from both sides of this equation and add 24 to both sides of this equation to get:\r
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\n" ); document.write( "\n" ); document.write( "a = 24 ***********************************************************\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "substitute 24 for a in the first equation to get:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "b = 2*24-12 which becomes:
\n" ); document.write( "b = 48-12 which becomes:
\n" ); document.write( "b = 36 ***********************************************************\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "substitute 36 for b in the second equation to get:\r
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\n" ); document.write( "\n" ); document.write( "c = 36 + 21 which becomes:
\n" ); document.write( "c = 57 ***********************************************************\r
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\n" ); document.write( "\n" ); document.write( "we get:
\n" ); document.write( "a = 24
\n" ); document.write( "b = 36
\n" ); document.write( "c = 57\r
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\n" ); document.write( "\n" ); document.write( "Now to see if this is accurate.\r
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\n" ); document.write( "\n" ); document.write( "Equation from the first transaction is:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(a-4) = (b+4)/2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "substitute 24 for a and 36 for b to get:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "24-4 = 36+4/2 which becomes:
\n" ); document.write( "20 = 40/2 which is true !!!!!\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Equation from the second transaction is:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(c+7) = (b-7) + 35\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "substitute 57 for c and 36 for b to get:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "57+7 = 36-7 + 35 which becomes:
\n" ); document.write( "64 = 29 + 35 which becomes:
\n" ); document.write( "64 = 64 which is true !!!!!\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Equation from the third transaction is:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "a+17 = c-17 + 1\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "substitute 24 for a and 57 for c to get:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "24+17 = 57-17+1 which becomes:
\n" ); document.write( "41 = 41 which is true !!!!!\r
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\n" ); document.write( "\n" ); document.write( "All equations are true so the answers must be good.\r
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\n" ); document.write( "\n" ); document.write( "Answers are:\r
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\n" ); document.write( "\n" ); document.write( "Alex has $24
\n" ); document.write( "Bobby has $36
\n" ); document.write( "Chris has $57\r
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